Learn Turkish: Bilgilendirmemiz icap eden resmî makam bugün çok meşgul. - The official authority that we are required to inform is very busy today.

The verb bilgilendirmek (to inform) takes the verbal noun suffix -me and the possessive -miz to become bilgilendirmemiz (our informing). Next, icap eden (which is necessary) follows it. Together, they act as a long adjective phrase modifying resmî makam, literally meaning "the official authority for which our informing is necessary."

Could I use gereken instead of icap eden here?

Yes, icap etmek and gerekmek are synonyms meaning "to be necessary." İcap etmek sounds a bit more formal, which pairs nicely with the formal context of a resmî makam (official authority). Saying bilgilendirmemiz gereken resmî makam is completely correct and means the exact same thing.

Why does resmî have a circumflex (hat) over the "i"?

The circumflex on î turns the noun root into the adjective resmî (official). It also changes the pronunciation slightly by lengthening the vowel, and importantly, it distinguishes the word from resmi (which would mean "the picture" in the accusative case, or "his/her picture").

Since we are informing the authority, why doesn't makam take an accusative ending?